Analysis-/synthesis-filtering system with efficient oddly-stacked singleband filter bank using time-domain aliasing cancellation

Abstract

An efficient implementation of oddly-stacked critically-sampled single sideband analysis/synthesis filter banks is achieved by application of a set of functions to time-domain and frequency-domain values before and after transformation. In one embodiment of an analysis filter bank, a forward pre-transform function groups blocks of N samples into blocks of 1/4N modified samples, a discrete transform generates frequency-domain coefficients in response to the modified samples, and a forward post-transform function generates spectral information in response to the frequency-domain transform coefficients. In one embodiment of a synthesis filter bank, an inverse pre-transform function groups spectral information into blocks of 1/4N frequency-domain transform coefficients, a discrete transform generates blocks of 1/4N time-domain transform coefficients in response to the frequency-domain transform coefficients, and an inverse post-transform function generates blocks of N time-domain samples in response to the time-domain transform coefficients. An implementation of an oddly-stacked Time Domain Aliasing Cancellation transform permits the length of the transformation to be adaptively selected.

I claim: 
     
       1. An analysis-filtering apparatus comprising input means for receiving an input signal, said input signal comprising input samples and representing audio or video information,   input buffer means for grouping said input samples into time-domain signal sample blocks of non-zero length N=a+b, where a and b are non-negative radix 4 integers and either a or b has a different value for at least two of said time-domain signal sample blocks, wherein adjacent blocks in a sequence of said time-domain signal sample blocks overlap one another, a respective time-domain signal sample block overlapping a previous block by a samples and overlapping a subsequent block by b samples,   analysis filter bank for generating spectral information in response to a respective one of said time-domain signal sample blocks, said analysis filter bank comprising forward pre-transform means for generating modified-sample blocks comprising at least one but not more than 1/4N complex-valued modified samples,   forward transform means for generating frequency-domain transform coefficients by applying one or more discrete transform functions to said modified-sample blocks, and     forward post-transform means for generating spectral information in response to said frequency-domain coefficients, and   output means for assembling a representation of said spectral information into a form suitable for transmission or storage.   
     
     
       2. An apparatus according to claim 1 wherein said spectral information is substantially equivalent to transform coefficients of an Oddly-stacked Time Domain Aliasing Cancellation transform. 
     
     
       3. An apparatus according to claim 1 wherein said forward pre-transform means comprises means for forming real-valued intermediate samples q(i) in response to said input samples x(i) according to ##EQU30## means for forming complex-valued intermediate samples g(n) according to   g(n)=q(N/2-1-2n)+jq(2n), and       means for generating said complex-valued modified samples by applying a complex rotation according to ##EQU31## and wherein said one or more discrete transform functions are substantially equivalent to a Discrete Fourier Transform.   
     
     
       4. An apparatus according to claim 3 wherein said forward post-transform means comprises means for forming complex-valued intermediate coefficients G(p) by applying a complex rotation to said frequency-domain coefficients according to ##EQU32## and means for generating said spectral information C(p) according to ##EQU33##   
     
     
       5. An apparatus according to any one of claims 1 through 4 wherein a and b are non-zero. 
     
     
       6. A synthesis-filtering apparatus comprising input means for receiving spectral information,   synthesis filter bank for generating time-domain signal samples in response to said spectral information, said synthesis filter bank comprising inverse pre-transform means for generating sets of frequency-domain transform coefficients in response to said spectral information, each of said sets comprising at least one but not more than 1/4N=1/4(a+b) coefficients, where a and b are non-negative radix 4 integers and either a or b has a different value in at least two of said sets,   inverse transform means for generating transform blocks comprising time-domain transform coefficients by applying one or more inverse discrete transform functions to said sets of frequency-domain transform coefficients, and   inverse post-transform means for generating time-domain signal sample blocks, each block of non-zero length N=a+b, wherein adjacent blocks in a sequence of said time-domain signal sample blocks overlap one another, a respective time-domain signal sample block overlapping a previous block by a samples and overlapping a subsequent block by b samples, and     output means for generating output samples representing audio or video information in response to said time-domain signal sample blocks.   
     
     
       7. An apparatus according to claim 6 wherein said spectral information is substantially equivalent to transform coefficients of an Oddly-stacked Time Domain Aliasing Cancellation transform. 
     
     
       8. An apparatus according to claim 6 wherein said one or more inverse discrete transform functions are substantially equivalent to an Inverse Discrete Fourier Transform and said inverse post-transform means comprises means for forming complex-valued intermediate samples g(p) by applying a complex rotation to said time-domain transform coefficients according to ##EQU34## and means for generating said time-domain signal samples x(n) according to ##EQU35##   
     
     
       9. An apparatus according to claim 8 wherein said inverse pre-transform means comprises means for forming complex-valued intermediate coefficients G(p) in response to said spectral information C(p) according to ##EQU36## means for generating said frequency-domain transform coefficients by applying a complex rotation according to ##EQU37##   
     
     
       10. An apparatus according to any one of claims 6 through 9 wherein a and b are non-zero. 
     
     
       11. A method for encoding and decoding samples representing audio or video information, said method comprising a) receiving an input signal, said input signal comprising input samples and representing audio or video information,   b) grouping said input samples into first time-domain signal sample blocks of non-zero length N=a+b, where a and b are non-negative radix 4 integers and either a or b has a different value for at least two of said time-domain signal sample blocks, wherein adjacent blocks in a sequence of said time-domain signal sample blocks overlap one another, a respective time-domain signal sample block overlapping a previous block by a samples and overlapping a subsequent block by b samples,   c) generating spectral information in response to a respective one of said first time-domain signal sample blocks by (1) generating modified-sample blocks comprising at least one but not more than 1/4N complex-valued modified samples, (2) generating first frequency-domain transform coefficients by applying one or more discrete transform functions to said modified-sample blocks, and (3) generating spectral information in response to said frequency-domain coefficients,   d) assembling an encoded representation of said spectral information into a form suitable for transmission or storage,   e) receiving said encoded representation of spectral information and obtaining reconstructed spectral information therefrom,   f) generating time-domain signal samples in response to said reconstructed spectral information by (1) generating sets of second frequency-domain transform coefficients in response to said spectral information, each of said sets comprising at least one but not more than 1/4N=1/4(a+b) coefficients, where either a or b has a different value in at least two of said sets, (2) generating transform blocks comprising time-domain transform coefficients by applying one or more inverse discrete transform functions to said sets of second frequency-domain transform coefficients, and (3) generating second time-domain signal sample blocks, each block of non-zero length N wherein adjacent blocks in said second time-domain signal sample blocks overlap one another, a respective second time-domain signal sample block overlapping a previous block by a samples and overlapping a subsequent block by b samples, and   g) generating output samples representing audio or video information in response to said second time-domain signal sample blocks.   
     
     
       12. A method according to claim 11 wherein said spectral information is substantially equivalent to transform coefficients of an Oddly-stacked Time Domain Aliasing Cancellation transform. 
     
     
       13. A method according to claim 11 wherein said generating modified-sample blocks comprises forming real-valued intermediate samples q(i) in response to said input samples x(i) according to ##EQU38## forming complex-valued intermediate samples g(n) according to   g(n)=q(N/2-1-2n)+jq(2n), and       generating said complex-valued modified samples by applying a complex rotation according to ##EQU39## said one or more discrete transform functions are substantially equivalent to a Discrete Fourier Transform, said one or more inverse discrete transforms are substantially equivalent to an Inverse Discrete Fourier Transform, and said generating second time-domain signal sample blocks comprises   forming complex-valued intermediate samples g(p) by applying a complex rotation to said time-domain transform coefficients according to ##EQU40## and generating said time-domain signal samples x(n) according to ##EQU41##   
     
     
       14. A method according to claim 13 wherein said generating spectral information comprises forming complex-valued intermediate coefficients G(p) by applying a complex rotation to said frequency-domain coefficients according to ##EQU42## and generating said spectral information C(p) according to ##EQU43## and wherein said generating sets of second frequency-domain transform coefficients comprises   forming complex-valued intermediate coefficients G(p) in response to said spectral information C(p) according to ##EQU44## generating said frequency-domain transform coefficients by applying a complex rotation according to ##EQU45##   
     
     
       15. A method according to any one of claims 11 through 14 wherein a and b are non-zero. 
     
     
       16. A synthesis-filtering method comprising the steps of: receiving spectral information,   generating sets of frequency-domain transform coefficients in response to said spectral information, each of said sets comprising at least one but not more than 1/4N=1/4(a+b) coefficients, where a and b are non-negative radix 4 integers and either a or b has a different value in at least two of said sets,   generating transform blocks comprising time-domain transform coefficients by applying one or more inverse discrete transform functions to said sets of frequency-domain transform coefficients, and   generating time-domain signal sample blocks, each block of non-zero length N=a+b, wherein adjacent blocks in a sequence of said time-domain signal sample blocks overlap one another, a respective time-domain signal sample block overlapping a previous block by a samples and overlapping a subsequent block by b samples, and   generating output samples representing audio or video information in response to said time-domain signal sample blocks.   
     
     
       17. A method according to claim 16 wherein said spectral information is substantially equivalent to transform coefficients of an Oddly-stacked Time Domain Aliasing Cancellation transform. 
     
     
       18. A method according to claim 16 wherein said one or more inverse discrete transform functions are substantially equivalent to an Inverse Discrete Fourier Transform and said step for generating time-domain signal sample blocks comprises forming complex-valued intermediate samples g(p) by applying a complex rotation to said time-domain transform coefficients according to ##EQU46## and generating said time-domain signal samples x(n) according to ##EQU47##   
     
     
       19. A method according to claim 18 wherein said step for generating sets of frequency-domain transform coefficients comprises forming complex-valued intermediate coefficients G(p) in response to said spectral information C(p) according to ##EQU48## generating said frequency-domain transform coefficients by applying a complex rotation according to ##EQU49##   
     
     
       20. A method according to any one of claims 16 through 19 wherein a and b are non-zero.